Tutorial on Bayesian Functional Regression Using Stan

TL;DR

This paper offers a comprehensive tutorial on implementing Bayesian functional regression with Stan, demonstrating comparable performance to frequentist methods and highlighting the flexibility and practical application to NHANES accelerometry data.

Contribution

It provides a detailed, step-by-step guide for Bayesian functional regression using Stan, filling a gap in accessible tutorials and extending the toolkit for functional data analysis.

Findings

Bayesian methods perform comparably to frequentist approaches in simulations.

Bayesian approaches offer greater modeling flexibility.

Application to NHANES data demonstrates practical utility.

Abstract

This manuscript provides step-by-step instructions for implementing Bayesian functional regression models using Stan. Extensive simulations indicate that the inferential performance of the methods is comparable to that of state-of-the-art frequentist approaches. However, Bayesian approaches allow for more flexible modeling and provide an alternative when frequentist methods are not available or may require additional development. Methods and software are illustrated using the accelerometry data from the National Health and Nutrition Examination Survey (NHANES).